Remember, the workspace rules don't actually allow you to tell the Savvyhead he can't build something he sets his mind to. You can, if you really want to, put such heavy restrictions on it that it can't be completed by the time you stop playing (but that doesn't sound like being a fan or making their lives not-boring to me!), but flat-out refusals are not permitted. So even without taking the improvement, he could build a robot! That's the Savvyhead's whole deal, he can build *anything* with enough time, jingle, and parts. Now, if he's willing to "pay" for his robot(s) in the form of an improvement, I'd go even easier on the restrictions.
I think I might be inclined to have him make the first robot, sort of a proof of concept, using the Workspace rules as normal. Then, once he's made one, he can easily make himself a gang of them offscreen just by taking the improvement. But you could certainly do it a number of other ways.